In many applications, information about a sample is determined by accumulating radiation from the sample over a period of time. A characteristic of the radiation, such as its energy profile or its diffraction pattern, can often be correlated to the type of material present in the sample. For example, when bombarded by electrons, a sample gives off characteristic x-rays whose energy correlates to the elements in the sample. Similarly, when bombarded with x-rays, crystals produce a characteristic diffraction pattern, and the frequency spectrum of gamma rays and other radiation are used by astronomers to learn about the composition of universe. The term “sample” is used broadly herein to include an object under observation.
In one widely used application, a scanning electron microscope can be used to determine the elemental composition of an unknown material. The scanning electron microscope (SEM) sends high-energy electrons smashing into material. When these electrons enter an atom, they can knock electrons out of the material. In the process, the first electron looses some energy, but can go on to smash into other atoms until it no longer has enough energy to continue doing so.
FIG. 1 shows an atom with electrons bound to the K, L, and M energy levels. An electron from the SEM is fired into this atom at a very high energy, dislodging one of the electrons from the atom. A very short time later, an electron from a higher energy level will fall into the created gap. In the process of falling into the lower energy K shell, it emits a single x-ray to balance the overall energy. The energy of the emitted x-ray depends on the initial location of the electron. If the electron originates from the L shell, then the radiation is designated as Kα radiation. If it originates from the M shell, then the radiation is designated as Kβ radiation, which has a higher energy than Kα radiation.
Alternatively, if an electron was dislodged from the L energy level, then a different set of x-rays may be omitted, depending from where the electron that will fill in the emptied position originates. FIG. 1 shows that an electron falling from the M shell to the L shell is associated with the emission of Lα a radiation.
The emitted x-rays are dependent on the specific starting and finishing energy levels. By analyzing the energy of the emitted x-ray, the type of the emitting atom can be determined. Each element in the periodic table has a specific set of energies corresponding to these x-ray energies. For example, the energy of the Kα radiation for carbon is 277 eV, compared to 523 eV for oxygen, or 98434 eV for uranium. If the electron from the SEM has a lower energy than this binding energy, then it is unable to dislodge the electron from the atom.
A complete list of binding energies for each element can be seen at http://xdb.lbl.gov/Section1/Table—1-2.pdf.
Alternatively, the electrons from the SEM may not enter an atom, but may be deflected away from an atom. This is caused by the negative electric charge on the electron being repelled by the negative charge of the electron cloud around the atoms.
FIG. 2 shows that the path of the electron is deflected away from an atom due to mutual electrostatic repulsion. The deflection of the path causes a small drop in energy of the high energy electron. This generates the Bremsstrahlung radiation. This effect occurs at lower intensities than the emission of x-rays seen in FIG. 1. However, it also occurs at all energy levels, rather than at discrete energy levels. The Bremsstrahlung radiation is an artefact of using an electron beam from a SEM. It must be taken into account when calculating the elemental composition. The shape of the Bremsstrahlung radiation depends on the average density of the material being analyzed, and is also affected by the standard based spectral analysis.
Standard Based Spectral Analysis
Standard based spectral analysis is a term used to describe the process of comparing the spectrum of an unknown mineral or element with a set of known spectra to determine the composition of the unknown spectrum in terms of the known spectra. This approach generates a solution that represents a multiplication factor for each of the known templates, which are then added together to synthesize the unknown spectrum.
FIG. 3 shows the spectrum of pyrite (FeS2). The spectrum comprises several peaks, and some regions of Bremsstrahlung radiation. There are some additional smaller peaks in this plot that are due to carbon (at 277 eV), and the iron La peak at 705 eV.
If one measures a sample of pure iron and pure sulphur, the spectra of these elements can be overlaid onto the spectrum of pyrite appropriately. The result is shown in FIG. 4. In particular, FIG. 4 shows that scaling the iron spectrum 44 to 42.0% and the sulphur spectrum 46 to 41.5% allows them to fit the peaks in the pyrite spectrum 42. These numbers are the peak ratios of these elements, because they represent the ratio of the area of each peak relative to a pure sample of the element. They do not represent the weight percentage of the material.
Matrix Corrections
The peak ratios obtained previously can be converted to a weight percentage using a standard matrix correction algorithm such as ZAF corrections. ZAF corrections account for differences in the atomic number (Z) of the elements, the absorption factor (A) of x-rays travelling through the material, and fluorescence (F) of x-rays from elements stimulating the emission of x-rays from other elements.
Issues with Standards-Based Spectral Analysis
In order to use standard-based spectral analysis, the operating conditions of the SEM must be determined. The factors that influence spectral analysis are the beam voltage, x-ray detector angles and beam current. The beam voltage affects the peaks that are stimulated and produce x-rays. As discussed previously in the text, if the beam voltage is lower than a particular binding energy for an elemental peak, then the peak is not present in the spectrum. In addition, the peaks that have a significantly lower binding energy are stimulated far more than peaks with binding energy close to the beam voltage. This results in the spectrum containing very large peaks in the low energy range, and very small peaks in the high energy range.
The x-ray detector angle affects the calculations for ZAF corrections, because it models the length of the path that the x-rays traverse through the material before reaching the detector.
The beam current affects the rate at which x-rays are generated. The standards need to be collected at the same current as the analysis is performed.
Overlapping Spectra
Some elemental spectra have peaks that overlap other element peaks. For instance, sulphur, lead and molybdenum have a peak at 2307 eV, 2342 eV and 2293 eV respectively. The elements have other peaks at different energies, but these spectra look very similar because the SEM beam voltage is too low to excite the molybdenum K peaks significantly (at 17481 eV). In addition, the lead K peaks are not excited at all because their energy is too high (74989 eV). This causes difficulties trying to resolve minerals that contain lead, sulphur or molybdenum. This is particularly difficult for galena which contains both lead and sulphur.
FIG. 5 shows the spectrum 52 for galena, and the scaled spectra 54 for lead and sulfur 56. The peaks for lead and sulfur overlap significantly, which makes the analysis of galena more difficult than pyrite. There are other elements whose elemental peaks overlap strongly and, thus, elemental artefacts may occur if one of these elements is present in the mineral. FIGS. 6 to 12 show further examples of such overlapping elements.
In particular, FIG. 7 shows that the platinum spectrum 74 and the zirconium spectrum 72 have an overlapping peak at 2.04 keV (channel 102). This causes problems in the analysis because it can incorrectly introduce zirconium to the analyzed composition if platinum is present. FIG. 8 shows the same type of overlapping peaks for the sodium spectrum 82 and the zinc spectrum 84. This causes sodium artefacts to be reported in minerals containing zinc. FIG. 9 shows that this type of overlap is also present for the aluminium spectrum 92 and the bromine spectrum 94. FIG. 10 shows the overlapping peak of the cadmium spectrum 102 and the uranium spectrum 104, which are very similar and could be confused at low concentration.
FIG. 11 shows the close overlap of the peaks of the silver spectrum 112 and the thorium spectrum 114. This close overlap causes problems at low count because the only difference between the spectra of these elements is the small peak at channel 648, which is invisible for low count spectra. This causes the identification of minerals containing either thorium or silver to incorrectly include the other element because of this overlap. Finally, FIG. 12 shows the overlapping peaks of the Yttrium spectrum 122 and the Iridium spectrum 124. Even such a relatively small overlap seems to cause problems for zirconia.
Low Count Spectral Analysis
The calculation of the constituent elements from a spectrum is not particularly difficult if high count spectra are used. For instance, FIG. 13 shows the spectrum of the mineral Albite (NaAlSi3O8) with the peaks shown very smoothly. The total number of x-rays collected to generate this spectrum was one million. In contrast, FIG. 14 shows the same mineral where the total number of x-rays collected was three hundred. In this figure, the jagged plot 142 shows the spectrum of the mineral, while the smooth plot 144 shows a fit of elemental spectra to the mineral. In the second example there is significant noise in the spectra and the peaks are not smooth. The elements reported for the low count spectra contain a number of artefacts that appear to be present based on the spectra, but are not present in the mineral. The task of analyzing spectra at low counts is more difficult because there is far more variability in the underlying spectrum, and the peaks of each element are not Gaussian. Therefore, the techniques used by existing approaches are unsuitable for low count spectral analysis for mineral identification, because they generally assume a smooth spectrum.
On the other hand, the accuracy of element quantification is lower for low-count spectra. If the elements shown in FIG. 13 and FIG. 14 are compared, it is apparent that the quantities of the four elements O, Na, Al and Si are slightly inaccurate at 300 counts.